Active shooter or assailant policies are available in addition to the broader entertainment-related coverages that include property, liability and business interruption.

“We provide the coverage either on a stand-alone basis or as a supplement within a terrorism policy,” said Ben Tucker, New York-based head of U.S. terrorism and political violence underwriting for XL Group Ltd., which does business as XL Catlin.

If a vehicle is used to harm people, “we would cover that scenario” under that policy, said Mr. Tucker.

The policy is designed “to respond in the immediate aftermath of an event and to help the insureds recover very quickly,” including by providing for employee counseling, job relocation, retraining, public relations costs and additional security.

“Our policy does not require physical loss or damages,” he said. Up to $35 million in limits can be provided, he said.

London-based Beazley P.L.C. also has a deadly weapons protection package whose three core pillars are prevention services, crisis management services and insurance cover to indemnify losses, according to the insurer.

It covers a wide variety of weapons, including explosive devices and medical instruments and any road vehicle used by an assailant to deliberately cause death or injury, according to the company.

Crisis management services are activated even if a weapon is just brandished, not just actually used, according to the insurer. Beazley offers up to $20 million capacity for its active shooter coverage, according to a spokeswoman.

Paul Marshall, managing director at managing general underwriter McGowan Program Administrators in Fairview Park, Ohio, whose firm underwrites these policies for both entertainment as well as workplace-related incidents, said his firm has underwriting arrangements with XL Catlin as well as with Lloyd’s of London under which it can provide up to $100 million in coverage.

Mr. Marshall said his firm’s coverage is evolving. Before the Manchester suicide bombing, “we would only pick up attacks with firearms. Now, we’re picking up explosive devices.”

Municipalities are also seeking coverage for incidents such as a drone attack, Mr. Marshall said. “We wish we weren’t talking about this, but this is what keeps people up at night,” he said.